A particle of mass $M$ is situated at the centre of spherical shell of mass M and radius $a$. The magnitude…

A particle of mass $M$ is situated at the centre of spherical shell of mass M and radius $a$. The magnitude of the gravitational potential at a point situated at $\frac{a}{2}$ distance from the centre, will be
  1. $\frac{2 G M}{a}$
  2. $\frac{3 G M}{a}$
  3. $\frac{4 G M}{a}$
  4. $\frac{G M}{a}$

Solution

$V_P=V_{\text {sphere }}+V_{\text {partical }}$ $\begin{aligned} & V_P=\frac{G M}{a}+\frac{G M}{a / 2} \\ & V=\frac{G M}{a}+\frac{2 G M}{a} \\ & V_P=\frac{3 G M}{a} \end{aligned}$

Asked in: NEET 2011 (Mains)

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